Along with the vacuume leaks I would check the carb. The accelerator pump might be out of adjustment or something else in the carb. Currently I have the same problem with mine and I just adjusted it and for 1 day so far it's ran fine but I have a holley on mine. Carb may be dirty also.

Well i am old school. i had a 1986 half ton pickup with 350 auto. with same problem. what i did was 86 the carb. and dist. put on a Qjet carb. and older h.e.i. dist. and did away with the computer.witch are the only two things it controls. i also swaped out the old lock up converter and trans. for 350 turbo. no more problems. it also ran a whole lot better. as far as the chk. engine light i just took the dash apart and took out the bulb.

Along with the vacuume leaks I would check the carb. The accelerator pump might be out of adjustment or something else in the carb. Currently I have the same problem with mine and I just adjusted it and for 1 day so far it's ran fine but I have a holley on mine. Carb may be dirty also.

If theres a sensation of bucking this is a transmission selonoid 15 to 30 part only automatics has this
now if theres trouble accelerating theres a couple things to look at
fuel filter fuel pump sending unit
clog in fuel injectors or vacume leaks start with break booster most of time this would be it

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There is a throttle valve positioner sensor located at the end of the throttle valve shaft on the right hand end of the shaft, the sensor then bolts to the throttle body as you face the engine from the front. A defective sensor will set the check engine light and give hesitation during acceleration.

http://engine-codes.com/p1125_chevrolet.html
According to that website above, its your Accelerator Position Pedal Sensor. If you have already replaced it check your wiring harness.
Here is a website that for your wiring diagram for your 2005 Chevy Suburban.

there are many things that could cause that from bad gas to weak fuel pump or dirty inline filter or timing chain could be weak or dirty intake or bad catalitic converter or no converter or even a vaccum line off or cracked or even a bad EGR valve so you see theres alot of things that cause poor exceleration or idle. Hope this was some what helpfull.